Moving to Germany

No, if she has income that exceeds 450 €/month, she has to get her own German health insurance.

She should also look into tax/social contribution laws for earning foreign income while resident in Germany.

The topic of working remotely for a foreign employer has been discussed several times on the forum. Please look for those threads!
Basically, she needs to register as freelancer/self-employed (because she has no German employer) and then pay her own health insurance (plus taxes and other compulsory liabilities) based on her world income.
The formalities for this are complex and might not be worth it for a small, occasional or temporary income.
Is she EU citizen and thus have the right to work here?

I started new thread as I could not find relevant information.
We are both EU citizens. The idea is for her to continue working remotely till she finds a job in Germany. Her income exceeds the 450 €/month but it is not enough to go for a private health insurance. She and her employer are paying taxes in another EU country and if she registers as a freelancer or self employed she has to pay additionally for an income already taxed in the EU. We can get her European Health Insurance Card but I read that it is valid up to 6 months and is hasn't not got fully coverage.

All EU countries have tax treaties with each other that give the right to tax income for work performed in a country to that country - regardless of where the employer sits or where/how that income is paid.
Also, anyone living and working in a country must follow that country‘s rules regarding health, social security etc. and contribute to that country‘s systems - although there might be exemptions for short-term engagements.
Thus she has to pay German taxes, German health, unemployment insurances and pension fund. She does not need to pay the same in her origin country!
Get a good international tax consultant to sort things out for you!